Timeline for Laplacian spectrum asymptotics in neck stretching
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2019 at 16:22 | comment | added | Neal | Quick sketch for why $h$ should be achieved by a cross-section in the neck part. Let $h_E = |E|/\min(A,B)$ for separating hypersurfaces $E$, with $A\cup B = M$ and $\partial A = \partial B = E$. Then $h = \inf_E h_E$. Since $h_{S\times 0} \to 0$, then $h$ must be achieved by a subsurface that enters the neck. Then show if a subsurface $E$ crosses between $M$ and the neck, it must have area that grows with a power of $T$, so $h_E$ will go as something like $1/\sqrt{T}$. That leaves subsurfaces contained within the neck, which have $h\sim 1/T$. | |
| Mar 15, 2019 at 14:13 | history | edited | macbeth | CC BY-SA 4.0 |
slightly better upper bound
|
| Mar 14, 2019 at 15:05 | history | answered | macbeth | CC BY-SA 4.0 |